Problem: Jessica works out for $\frac{5}{6}$ of an hour every day. To keep her exercise routines interesting, she includes different types of exercises, such as squats and sit-ups, in each workout. If each type of exercise takes $\frac{5}{12}$ of an hour, how many different types of exercise can Jessica do in each workout?
Answer: To find out how many types of exercise Jessica could do in each workout, divide the total amount of exercise time ( $\frac{5}{6}$ of an hour) by the amount of time each exercise type takes ( $\frac{5}{12}$ of an hour). $ \dfrac{{\dfrac{5}{6} \text{ hour}}} {{\dfrac{5}{12} \text{ hour per exercise}}} = {\text{ number of exercises}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of ${\dfrac{5}{12} \text{ hour per exercise}}$ is ${\dfrac{12}{5} \text{ exercises per hour}}$ $ {\dfrac{5}{6}\text{ hour}} \times {\dfrac{12}{5} \text{ exercises per hour}} = {\text{ number of exercises}} $ $ \dfrac{{5} \cdot {12}} {{6} \cdot {5}} = {\text{ number of exercises}} $ Reduce terms with common factors by dividing the $5$ in the numerator and the $5$ in the denominator by $5$ $ \dfrac{{\cancel{5}^{1}} \cdot {12}} {{6} \cdot {\cancel{5}^{1}}} = {\text{ number of exercises}} $ Reduce terms with common factors by dividing the $12$ in the numerator and the $6$ in the denominator by $6$ $ \dfrac{{1} \cdot {\cancel{12}^{2}}} {{\cancel{6}^{1}} \cdot {1}} = {\text{ number of exercises}} $ Simplify: $ \dfrac{{1} \cdot {2}} {{1} \cdot {1}} = {2} $ Jessica can do 2 different types of exercise per workout.